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A048911
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Indices of square numbers which are also 9-gonal.
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2
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1, 3, 33, 91, 989, 2727, 29637, 81719, 888121, 2448843, 26613993, 73383571, 797531669, 2199058287, 23899336077, 65898365039, 716182550641, 1974751892883, 21461577183153, 59176658421451, 643131132943949
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| From Ant King, Nov 18 2011: (Start)
lim( n -> Infinity, a(2n+1)/a(2n)) = 1/25 * (137 + 36 * sqrt(14))
lim( n -> Infinity, a(2n)/a(2n-1)) = 1/25 * (39 + 8 * sqrt(14))
(End)
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| From Ant King, Nov 18 2011: (Start)
a(n) = 30 * a(n-2) - a(n-4).
GF: x * (1 + x) ^ 3 / (1 - 30 * x ^ 2 + x ^ 4)
Let p = 8 * sqrt(7) + 9 * sqrt(14) - 7 * sqrt(2) - 28 and q = 7 * sqrt(2) + 9 * sqrt(14) - 8 * sqrt(7) - 28. Then
a(n) = 1/112 * ( ( p + q * (-1) ^ n) * ( 2 * sqrt(2) + sqrt(7)) ^ n - ( p - q * (-1) ^ n) * ( 2 * sqrt(2) - sqrt(7)) ^ ( n - 1) )
a(n) = floor ( 1/112 * ( p + q * (-1) ^ n) * ( 2 * sqrt(2) + sqrt(7)) ^ n )
(End)
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MATHEMATICA
| LinearRecurrence[ {0, 30, 0, - 1 }, { 1, 3, 33, 91 } , 21 ] (* Ant King, Nov 18 2011 *)
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CROSSREFS
| Cf. A048910, A036411.
Sequence in context: A139222 A123049 A153783 * A089015 A062215 A132122
Adjacent sequences: A048908 A048909 A048910 * A048912 A048913 A048914
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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